Generalized derivations on Lie ideals in prime rings

Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] in Z, for all u in U, then U subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v in U, then U subset Z. (iii) f([u,v])=pm lbrack u,v], for all u,vin U, then U subset Z.